论文标题
数据驱动的两阶段圆锥优化，具有零一个不确定性
Data-driven two-stage conic optimization with zero-one uncertainties
论文作者
论文摘要
我们在两阶段凸圆锥优化问题中解决高维零随机参数。此类参数通常代表网络元素的故障，并在几种应用中构成罕见的高影响力随机事件。鉴于参数的稀疏训练数据集，我们使用以经验分布为中心的Wasserstein歧义歧义性来激励和研究问题的分布强劲表述。我们提出了该问题的简单，可拖延和保守的近似，可以有效地计算并迭代地改进。我们的方法依赖于一个重新制定的，该重新构造优化了可代表的混合式圆锥编程的凸壳，然后使用提升和项目的技术对该凸面船体进行了近似。我们说明了我们方法在非线性最佳功率流和多商品网络设计问题上的实际生存能力和样本外性能，这些问题受随机意外情况的影响，我们报告的改善比现有样品平均近似值和两阶段的两阶段良好优化方法的改善。
We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications. Given a sparse training dataset of the parameters, we motivate and study a distributionally robust formulation of the problem using a Wasserstein ambiguity set centered at the empirical distribution. We present a simple, tractable, and conservative approximation of this problem that can be efficiently computed and iteratively improved. Our method relies on a reformulation that optimizes over the convex hull of a mixed-integer conic programming representable set, followed by an approximation of this convex hull using lift-and-project techniques. We illustrate the practical viability and strong out-of-sample performance of our method on nonlinear optimal power flow and multi-commodity network design problems that are affected by random contingencies, and we report improvements of up to 20\% over existing sample average approximation and two-stage robust optimization methods.
